Tail Inference for a Law in a Max-Semistable Domain of Attraction

2000 Mathematics Subject Classification: 62G32, 62G05.

Statistical Inference for Processes Depending on Environments and Application in Regenerative Processes

We build the Conditional Least Squares Estimator of 0 based on the observation of a single trajectory of {Zk,Ck}k, and give conditions ensuring its strong consistency. The particular case of general linear models according to 0=( 0, 0) and among them, regenerative processes, are studied more particularly. In this frame, we may also prove the consistency of the estimator of 0 although it belongs to an asymptotic negligible part of the model, and the asymptotic law of the estimator may also be calculated.

Inference of helicopter airframe condition

The goal of this paper is to model normal airframe conditions for helicopters in order to detect changes. This is done by inferring the flying state using a selection of sensors and frequency bands that are best for discriminating between different states. We used non-linear state-space models (NLSSM) for modelling flight conditions based on short-time frequency analysis of the vibration data and embedded the models in a switching framework to detect transitions between states. We then created a density model (using a Gaussian mixture model) for the NLSSM innovations: this provides a model for normal operation. To validate our approach, we used data with added synthetic abnormalities which was detected as low-probability periods. The model of normality gave good indications of faults during the flight, in the form of low probabilities under the model, with high accuracy (>92 %). © 2013 IEEE.

Wireless power and data transfer via a common inductive link using frequency division multiplexing

For wireless power transfer (WPT) systems, communication between the primary side and the pickup side is a challenge because of the large air gap and magnetic interferences. A novel method, which integrates bidirectional data communication into a high-power WPT system, is proposed in this paper. The power and data transfer share the same inductive link between coreless coils. Power/data frequency division multiplexing technique is applied, and the power and data are transmitted by employing different frequency carriers and controlled independently. The circuit model of the multiband system is provided to analyze the transmission gain of the communication channel, as well as the power delivery performance. The crosstalk interference between two carriers is discussed. In addition, the signal-to-noise ratios of the channels are also estimated, which gives a guideline for the design of mod/demod circuits. Finally, a 500-W WPT prototype has been built to demonstrate the effectiveness of the proposed WPT system.

Vocabulary learning through use of the picture-word inductive model for young English learners in China: A mixed methods examination using Cognitive Load Theory

English has been taught as a core and compulsory subject in China for decades. Recently, the demand for English in China has increased dramatically. China now has the world's largest English-learning population. The traditional English-teaching method cannot continue to be the only approach because it merely focuses on reading, grammar and translation, which cannot meet English learners and users' needs (i.e., communicative competence and skills in speaking and writing). ^ This study was conducted to investigate if the Picture-Word Inductive Model (PWIM), a new pedagogical method using pictures and inductive thinking, would benefit English learners in China in terms of potential higher output in speaking and writing. With the gauge of Cognitive Load Theory (CLT), specifically, its redundancy effect, I investigated whether processing words and a picture concurrently would present a cognitive overload for English learners in China. ^ I conducted a mixed methods research study. A quasi-experiment (pretest, intervention for seven weeks, and posttest) was conducted using 234 students in four groups in Lianyungang, China (58 fourth graders and 57 seventh graders as an experimental group with PWIM and 59 fourth graders and 60 seventh graders as a control group with the traditional method). No significant difference in the effects of PWIM was found on vocabulary acquisition based on grade levels. Observations, questionnaires with open-ended questions, and interviews were deployed to answer the three remaining research questions. A few students felt cognitively overloaded when they encountered too many writing samples, too many new words at one time, repeated words, mismatches between words and pictures, and so on. Many students listed and exemplified numerous strengths of PWIM, but a few mentioned weaknesses of PWIM. The students expressed the idea that PWIM had a positive effect on their English teaching. ^ As integrated inferences, qualitative findings were used to explain the quantitative results that there were no significant differences of the effects of the PWIM between the experimental and control groups in both grade levels, from four contextual aspects: time constraints on PWIM implementation, teachers' resistance, how to use PWIM and PWIM implemented in a classroom over 55 students.^

The Communication of Inductive Inferences

Postprint

Strong inference from transect sign surveys : combining spatial autocorrelation and misclassification occupancy models to quantify the detectability of a recovering carnivore

Funding — Forest Enterprise Scotland and the University of Aberdeen provided funding for the project. The Carnegie Trust supported the lead author, E. McHenry, in this research through the award of a tuition fees bursary.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

Vocabulary Learning through Use of the Picture-Word Inductive Model for Young English Learners in China: A Mixed Methods Examination Using Cognitive Load Theory

English has been taught as a core and compulsory subject in China for decades. Recently, the demand for English in China has increased dramatically. China now has the world’s largest English-learning population. The traditional English-teaching method cannot continue to be the only approach because it merely focuses on reading, grammar and translation, which cannot meet English learners and users’ needs (i.e., communicative competence and skills in speaking and writing). This study was conducted to investigate if the Picture-Word Inductive Model (PWIM), a new pedagogical method using pictures and inductive thinking, would benefit English learners in China in terms of potential higher output in speaking and writing. With the gauge of Cognitive Load Theory (CLT), specifically, its redundancy effect, I investigated whether processing words and a picture concurrently would present a cognitive overload for English learners in China. I conducted a mixed methods research study. A quasi-experiment (pretest, intervention for seven weeks, and posttest) was conducted using 234 students in four groups in Lianyungang, China (58 fourth graders and 57 seventh graders as an experimental group with PWIM and 59 fourth graders and 60 seventh graders as a control group with the traditional method). No significant difference in the effects of PWIM was found on vocabulary acquisition based on grade levels. Observations, questionnaires with open-ended questions, and interviews were deployed to answer the three remaining research questions. A few students felt cognitively overloaded when they encountered too many writing samples, too many new words at one time, repeated words, mismatches between words and pictures, and so on. Many students listed and exemplified numerous strengths of PWIM, but a few mentioned weaknesses of PWIM. The students expressed the idea that PWIM had a positive effect on their English teaching. As integrated inferences, qualitative findings were used to explain the quantitative results that there were no significant differences of the effects of the PWIM between the experimental and control groups in both grade levels, from four contextual aspects: time constraints on PWIM implementation, teachers’ resistance, how to use PWIM and PWIM implemented in a classroom over 55 students.

Exploring Seventh Graders’ Perceptions of the Picture-word Inductive Model to their English Narrative Writing in China

In this exploratory study, the researcher interviewed 30 seventh graders in China about their perceptions of the newly tried method, Picture-word Inductive Model (PWIM), to their English narrative writing. Many student participants listed and exemplified positive influence of PWIM on their narrative writing in and from the PWIM trial.

Likelihood-Based Inference for Partially Observed Multi-Type Markov Branching Processes

Thesis (Ph.D.)--University of Washington, 2016-08

Finite Population Inference for Causal Parameters

Thesis (Ph.D.)--University of Washington, 2016-08